----------------------------------------------------------------------------- A v v i s o d i S e m i n a r i o ----------------------------------------------------------------------------- Martedì 14 Gennaio, ore 10:30am -----------------------------------------------------------------------------

Stanza 34 Dipartimento di Scienze Statistiche Sapienza Università di Roma

ELENA KARACHANSKAYA (Pacific National University, Khabarovsk)

terrà un seminario dal titolo

THE INVARIANT METHOD IN THE THEORY OF STOCHASTIC DIFFERENTIAL EQUATIONS AND ITS APPLICATIONS FOR THE CONTROL PROGRAM PROBLEMS

tutti gli interessati sono invitati a partecipare.

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Pierpaolo Brutti

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Summary

We consider two types of invariants (geometric and integral), which are connected with the theory of stochastic differential equations (SDEs). The geometric invariants are the fixed length of a random chain and the constant radius of a sphere, which is the surface for random walks (for example, in the case of a turning diffusion). The integral invariants are represented as integrals of kernel functions of integral invariants on the whole space. These kernel functions are solutions of SDEs, which were obtained and discussed. Furthermore, kernel functions will be used for deriving the first global stochastic integral, for constructing the program control (with probability one) for stochastic dynamical systems on deterministic manifold based on Brownian motion with Poisson jumps, and for obtaining the Kolmogorov equations.